Saturday, October 17, 2015

Rubba Dub Dub, CO2 in Three Tubs


ATTP has been beating a bit on the carbon cycle, something Eli has talked about before.  (Go ahead, Google is your friend bunnies)  Some of that discussion, well it was ok, but a simple, grandmother level explanation came to Eli's mind.

There are lots of illustrations of the carbon cycle, most of them, like this one from GLOBE, with too much detail.


The carbon cycle is characterized by three times.  The first is the rapid equilibration between the three surface reservoirs, the upper part of the ocean, called the surface ocean in the figure above, the atmosphere and what Eli calls the surface biosphere, vegetation and topsoil.  There are about the same size, within quibble distance of each other, and the interchange takes about five years.  This is the subject of Eli's first post.

The second is the time needed to move carbon, mostly as animal shells falling to the bottom from the upper ocean into the deeps.  The deep ocean reservoir is much bigger than the each of the surface reservoirs, more than thirty times as much, but the time needed to move carbon from the surface ocean to the bottom of the sea is a few hundred years.

The third is the incorporation of carbon dioxide into rocks, which is really slow, like over tens of thousands or years or more.

Because things happen at different rates, one can discuss each part of the cycle separately.  Let the MOOC de Rabett start by looking at the fast processes.  A really important insight is that two of the reservoirs, the surface biosphere and the ocean, are NOT connected to each other, but are linked through the atmosphere.  A zeroth level model of this looks like


Now we can ask what happens when Exxon encourages pouring a bunch of CO2 into the atmosphere


Keep this one on your phone to explain things to your favorite uncle over the upcoming holidays.

Anybunny wanting a more "mathematical" description of this could write out a series of rate equations and solve them (Excel with Euler integration works).  In this system, Cx(t) is the amount of carbon in each of the reservoirs at time t, and kxy is the rate of exchange from reservoir x to y.  E(t) describes the rate that carbon (dioxide) is injected into the atmosphere at time t.  Note that the total amount of carbon in the three fast reservoirs is a constant


19 comments:

Nick Stokes said...

Eli,
"The second is the time needed to move carbon, mostly as animal shells falling to the bottom from the upper ocean into the deeps."

It seems to me that as well as tracking C, we should be tracking acid/base. When C is burnt, it creates, in the Lewis sense, two vacancies for electron pairs. And CO2 will be on the loose until they are filled. If we could dig up Gtons of NaOH, the CO2 could be absorbed, and problem over. But base is in short supply. The only bulk base we can make is CaO. But that produces 1 CO2 for each CaO.

Sinking CaCO3 doesn't help that problem. CaCO3 can dissolve, providing the electron pairs. But that denudes shellfish. It seems to me that the only longterm source of electron pairs is your third process, from breaking down basic rock. And that is really slow.

andthentheresphysics said...

In case it wasn't obvious, my posts were partly motivated by an exchange with Nic Lewis who seems to think that only a small fraction of our emissions would remain in the atmosphere for a long time. Unless I misunderstand what he means by "small fraction" I think it suggests that he doesn't understand what you're illustrating in the animation at the end of your post.

Fernando Leanme said...

The overall process rate is somewhat irrelevant. What counts is the rate change as a function of CO2 concentration in the atmosphere, and ocean pH. Thus far the carbon sequestration by sinks seems to track atmospheric concentration. This implies CO2 concentration will peak at around 630 ppm. This can be reduced by a smart properly bought renewables and nuclear power investment program, hopefully supplemented by geoengineering of some sort (this has to be given more research priority).

andthentheresphysics said...

Thus far the carbon sequestration by sinks seems to track atmospheric concentration. This implies CO2 concentration will peak at around 630 ppm.
According the SPM, this would require that we emit no more than about 600GtC. It also means that atmospheric CO2 would remain above 450ppm for thousands of years, and suggests that we'd be committed to around 2.5C of warming above pre-industrial.

8c7793aa-15b2-11e5-898a-67ca934bd1df said...

The only real solution is to crack the carbon, reduce it back to diamond or a multitude of lower polymorphs, polytypes and allotropes and then export it to space in the form of cryogenic fuel tanks. That of course will require a great deal of two dimensional thin film nanostructures of course, and right off the bat I can think of several.

Or just use it up all here on earth. Do please keep it underground then.

Rob Painting said...

The second is the time needed to move carbon, mostly as animal shells falling to the bottom from the upper ocean into the deeps.

Eli is probably thinking of the biological carbon pump here (soft organic tissue), not the carbonate pump (shells). The biological production of carbohydrates, and the incorporation of this CO2 into soft organic tissue, draws down CO2 dissolved in surface waters. Calcification (shell formation) on the other hand releases CO2 into surface waters.

Hank Roberts said...

Or, it's like a library:
https://izenmeme.wordpress.com/2015/10/12/insubstantial-analogies/#more-403

Susan Anderson said...

I like grandmother level explanations, since in age if not in fact I am of grandmother age and comprehension level.

However, the nonsense of exporting carbon into space requires comment.

What exactly are you planning to use for that export? More carbon fuels? Something combustible? Nuclear? This is the kind of thinking that is unhelpful to an extreme.

EliRabett said...

Fernando is planning to make the excursion.

8c7793aa-15b2-11e5-898a-67ca934bd1df said...

"What exactly are you planning to use for that export?"

Well since we can demonstrably crack carbon dioxide and even water, using solar energy, then both hydrogen and methane work for me. There are issues with hydrogen and water vapor in the stratosphere that will need to be addressed, but as I said, leaving the carbon in the ground and then reducing down the atmospheric carbon dioxide into carbon is fine, as long as you put the resulting widespread carbon products underground and not on the surface where we have this biosphere thing.

Helpful or not, this is your new reality.

mj said...

The expression for dC_A/dt is incorrect because it simply repeats twice the exchange with the
B reservoir and does not include the exchange with the O reservoir.

EliRabett said...

Thank you mj. Copying error in latex eq editor or at least that is what Eli is saying

mj said...

Oh no. The expression for dC_A/dt is now missing E(t).

EliRabett said...
This comment has been removed by the author.
EliRabett said...

Effing Gremlins. Knew there was a good reason to avoid LaTex. Thanks

Hank Roberts said...

> Rob Painting ...
> Calcification (shell formation) on the other hand releases CO2

Wait. What? That would suggest that dissolving pteropods ... no.

ncdave4life said...

Rob Painting wrote, "Calcification (shell formation) on the other hand releases CO2 into surface waters"

Huh? How can that be? I'm not a biologist, but seashells are made mostly of calcium carbonate. So shell formation absorbs carbon. That's why if you dissolve a seashell with HCl, it bubbles off CO2, like this:
https://www.youtube.com/watch?v=c5nG-Z-WSbg

Hank Roberts said...

> Rob Painting wrote, "Calcification (shell formation) on the other hand
> releases CO2 into surface waters"

Did he go away after making that post?
Citation badly needed.

EliRabett said...

Ankh, it's the carbonate counter pump

http://rabett.blogspot.com/2015/11/the-deep-blue-sea.html